Given the fact this young budgie hatched with such an apparent and severe disability/deformity, it's not at all advisable that you let this chick's parents to breed again, because the chances for you to get more chicks with varying disabilities/deformities are much higher too and it's not worth to risk this.
This is why it's so important to choose suitable pairings from completely unrelated birds. This is one of consequences typically seen when inbreeding budgies.
To help the chick to wean you can offer egg food, by hard boiling an egg and mashing it all up. You can also add some finely chopped up vegetables to the mix. Offering sprouted seed is also a good option.
I'm wishing you the best of luck at the vet's.
Depending on the case, your budgie may need regular trims and beak adjustments.
Given the condition, your young budgie will most likely require special needs for the rest of his life and you will have to keep a close eye on him to see how well he is eating his meals.
RIP sweet Tito (Summer 2008 - January 17th 2013).
You are missed and never will be forgotten.